AbstractThe notions ofos{o}_{s}-convergence andS∗{S}^{\ast }-doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence andS∗{S}^{\ast }-doubly continuous posets, respectively. We first consider the relationship betweenos{o}_{s}-convergence and B-topology and show that the topology induced byos{o}_{s}-convergence according to the standard topological approach is the B-topology precisely. Then, the topological characterization for theS∗{S}^{\ast }-doubly quasicontinuity is presented. It is proved that a poset isS∗{S}^{\ast }-doubly quasicontinuous iff the poset equipped with the B-topology is locally hyperclosed iff the lattice of all B-open subsets of the poset is hypercontinuous. Finally, the order theoretical condition for theos{o}_{s}-convergence being topological is given and the complete regularity of B-topology onS∗{S}^{\ast }-doubly quasicontinuous posets is explored.